长度为奇素数的完备高斯整数序列构造法

李玉博; 陈邈; 刘涛; 张颖

doi:10.11959/j.issn.1000-436x.2018230

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长度为奇素数的完备高斯整数序列构造法

学术通信 | 更新时间：2024-06-05

- 长度为奇素数的完备高斯整数序列构造法
- Constructions of perfect Gaussian integer sequences of odd prime length
- 通信学报 2018年39卷第11期页码：190-197
- 作者机构：
  
  1. 燕山大学信息科学与工程学院，河北秦皇岛 066004
  2. 河北省信息传输与信号处理重点实验室，河北秦皇岛 066004
- 作者简介：
  
  [ "李玉博（1985−），男，河北衡水人，博士，燕山大学讲师，主要研究方向为编码理论、序列设计、信息处理。" ]
  [ "陈邈（1993−），男，河北唐山人，燕山大学硕士生，主要研究方向为无线通信、序列设计。" ]
  [ "刘涛（1987−），女，河北秦皇岛人，燕山大学博士生，主要研究方向为组合编码、信息安全、序列设计。" ]
  [ "张颖（1997−），女，山西平定县人，本科生，主要研究方向为无线通信、编码理论。" ]
- 基金信息：
  
  国家自然科学基金资助项目(61501395)
- DOI：10.11959/j.issn.1000-436x.2018230
  中图分类号： TN911.2
- 网络出版日期：2018-11，
  
  纸质出版日期：2018-11-25
- 稿件说明：
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李玉博, 陈邈, 刘涛, 等. 长度为奇素数的完备高斯整数序列构造法[J]. 通信学报, 2018,39(11):190-197.

Yubo LI, Miao CHEN, Tao LIU, et al. Constructions of perfect Gaussian integer sequences of odd prime length[J]. Journal on communications, 2018, 39(11): 190-197.
李玉博, 陈邈, 刘涛, 等. 长度为奇素数的完备高斯整数序列构造法[J]. 通信学报, 2018,39(11):190-197. DOI： 10.11959/j.issn.1000-436x.2018230.

Yubo LI, Miao CHEN, Tao LIU, et al. Constructions of perfect Gaussian integer sequences of odd prime length[J]. Journal on communications, 2018, 39(11): 190-197. DOI： 10.11959/j.issn.1000-436x.2018230.

摘要

提出一类基于分圆类构造完备高斯整数序列的方法。分别通过有限域GF(p)上的2阶和4阶分圆类，构造得到自由度分别为3和5的高斯整数序列，序列长度为奇素数，该序列具有良好的完备自相关性能。该构造方法解决了以往利用分圆类计算复杂度较高，不易求解的问题，简化了序列的生成方法。该序列在无线通信中具有良好的应用前景。

Abstract

Constructions of perfect Gaussian integer sequences (PGIS) based on the cyclotomic classes were proposed.The PGIS with degree 3 and 5 were constructed respectively from the cyclotomic classes of order 2 and 4.The presented sequences with odd prime length have ideal autocorrelations.The methods solved the problem that the traditional constructions of PGIS from the cyclotomic classes have high computational complexity.As a result

this kind of sequences will be useful in the applications of wireless communications.

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references

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